I've been replacing all of my Pampered Chef non-stick cookware with a combination of : cast iron, stainless steel and few pieces of Le Creuset.
It depends on what you're looking for. Cast iron for instance, can't go in the dishwasher. But the stainless and LeCreuset can. The stainless might loose it's new, pretty finish; but it will still cook the same. Le Creuset is dishwasher safe too. That said, I just hand wash my stainless and LeCreuset.
Also, you could consider replacing non-stick bakeware with either glass (like Pyrex) or stoneware.
We have Lagostina as do my mom and sister though ours are a newer style. Ours has 6 pots, lids and a steamer. They are aluminum between ss layers which I didn't like but it's hard to find sets with copper bottoms. I have a store brand 10" or 12" frying pan that is copper bottom. It's heavy but works great.
The handles and lids are both ss, neither one get hot while cooking.
I don't find them hard to take care of. IF anything is stuck on I soak in water, or put some water in and heat it up on the burner. I use the square plastic thing that came with my stone pan to scape off anything tough though I find heating up works better.
Lemon juice, or cooking with things like lemon juice helps to restore the shine.
I've read that the copper bottoms don't do a whole lot for heat distribution and are high maintenance and they're mainly for show - I've read conflicting info on the previously mentioned - pure stainless is fine and most of the time cheaper.
Here's some good links - most are these answers are from chefs and food science types:
we use the stainless (not non-stick) All Clad, which costs a ton of money... but, we got it early in our marriage and i figure it will last us and probably another family for a really really long time. it has rivited handles (handles w/ screws will rust and come loose over time) and they can all go in the oven, the long handles, although stainless, don't get hot, it doesn't keep the shiny new finish forever, you can use Barkeepers Friend on it to keep it looking pretty nice. and it cooks VERY evenly. we had a stainless set before this one w/ the thick bottoms that are glued (i think) on, and you would think they would cook really well because of the thick bottom, but the All Clad is nice and thick all the way up the sides as well.
i wouldn't trade it for any other cookware, and when i use other people's cookware, i can really notice the difference, especially when using a fry pan.
if you are looking to replace, do it a piece at a time, and get a fry pan first and make scrambled eggs, you will be in heaven!!